Duke submitted his project to Pegasus and played a game with him in order to show him the potential of the game. Pegasus won that game easily making Duke surprised. It is probable that Pegasus used his mind reading tricks to know how to play but according to Yami Yugi it was more like Pegasus was playing the game he invented in the first place.
Pegasus accepted to fund the game, but it was not because he liked it. His reasoning was that the game was going to make Duel Monsters look really exciting in comparison to the piece of trash game.
After Yugi defeated Pegasus and he fell into a coma (or... died by getting both eyes pulled by Florence), Duke developed a huge grudge to him because the game was not going to get funds.
Yami Yugi played a game with Duke in order to make Joey free of a (well deserved) bet. Yami won easily, which was not really a wonder considering the huge resemblance to Duel Monsters.
According to Duke, the game is not like Duel Monsters because his game "has dice in it".
After the episode in which the game was played, nobody (except for Duke) even remembers the game, until Tristan tells Serenity that its the same thing as duel monsters.